Hamas has said since the collapse that it will not resume negotiations as long as the fighting continues.
The three men have been identified by Israel as 79-year-old Chaim Peri, 80-year-old Yoram Metzger and 84-year-old Amiram Cooper.
Israel and Hamas ended a week-long cease-fire early in December that included daily exchanges of hostages taken by Hamas in the October attack for prisoners held in Israeli jails.